UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl) UvA-DARE (Digital Academic Repository) The M 4 Core Project with HST - III. Search for variable stars in the primary field Nascimbeni, V.; Bedin, L.R.; Heggie, D.C.; van den Berg, M.; Giersz, M.; Piotto, G.; Brogaard, K.; Bellini, A.; Milone, A.P.; Rich, R.M.; Pooley, D.; Anderson, J.; Ubeda, L.; Ortolani, S.; Malavolta, L.; Cunial, A.; Pietrinferni, A. DOI 10.1093/mnras/stu930 Publication date 2014 Document Version Final published version Published in Monthly Notices of the Royal Astronomical Society Link to publication Citation for published version (APA): Nascimbeni, V., Bedin, L. R., Heggie, D. C., van den Berg, M., Giersz, M., Piotto, G., Brogaard, K., Bellini, A., Milone, A. P., Rich, R. M., Pooley, D., Anderson, J., Ubeda, L., Ortolani, S., Malavolta, L., Cunial, A., & Pietrinferni, A. (2014). The M 4 Core Project with HST - III. Search for variable stars in the primary field. Monthly Notices of the Royal Astronomical Society, 442(3), 2381-2391. https://doi.org/10.1093/mnras/stu930 General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Download date:24 Aug 2021
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UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)
UvA-DARE (Digital Academic Repository)
The M 4 Core Project with HST - III. Search for variable stars in the primary field
Nascimbeni, V.; Bedin, L.R.; Heggie, D.C.; van den Berg, M.; Giersz, M.; Piotto, G.; Brogaard,K.; Bellini, A.; Milone, A.P.; Rich, R.M.; Pooley, D.; Anderson, J.; Ubeda, L.; Ortolani, S.;Malavolta, L.; Cunial, A.; Pietrinferni, A.DOI10.1093/mnras/stu930Publication date2014Document VersionFinal published versionPublished inMonthly Notices of the Royal Astronomical Society
Link to publication
Citation for published version (APA):Nascimbeni, V., Bedin, L. R., Heggie, D. C., van den Berg, M., Giersz, M., Piotto, G.,Brogaard, K., Bellini, A., Milone, A. P., Rich, R. M., Pooley, D., Anderson, J., Ubeda, L.,Ortolani, S., Malavolta, L., Cunial, A., & Pietrinferni, A. (2014). The M 4 Core Project with HST- III. Search for variable stars in the primary field. Monthly Notices of the Royal AstronomicalSociety, 442(3), 2381-2391. https://doi.org/10.1093/mnras/stu930
General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s)and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an opencontent license (like Creative Commons).
Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, pleaselet the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the materialinaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letterto: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. Youwill be contacted as soon as possible.
The M 4 Core Project with HST – III. Search for variable starsin the primary field�
V. Nascimbeni,1† L. R. Bedin,1 D. C. Heggie,2 M. van den Berg,3,4
M. Giersz,5 G. Piotto,1,6 K. Brogaard,7,8 A. Bellini,9 A. P. Milone,10
R. M. Rich,11 D. Pooley,12,13 J. Anderson,9 L. Ubeda,9 S. Ortolani,1,6
L. Malavolta,1,6 A. Cunial1,6 and A. Pietrinferni14
1INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy2School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Kings Buildings, Edinburgh EH9 3JZ, UK3Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, the Netherlands4Harvard–Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA5Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warsaw, Poland6Dipartimento di Fisica e Astronomia ‘Galileo Galilei’, Universita di Padova, Vicolo dell’Osservatorio 3, I-35122 Padova, Italy7Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade, 8000 Aarhus C, Denmark8Department of Physics and Astronomy, University of Victoria, PO Box 3055, Victoria, BC V8W 3P6, Canada9Space Telescope Science Institute, 3800 San Martin Drive, Baltimore, MD 21218, USA10Research School of Astronomy and Astrophysics, The Australian National University, Cotter Road, Weston, ACT 2611, Australia11Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA12Department of Physics, Sam Houston State University, Huntsville, TX 77341, USA13Eureka Scientific, Inc., 2452 Delmer Street, Suite 100, Oakland, CA 94602, USA14INAF – Osservatorio Astronomico di Teramo, Via M. Maggini, I-64100 Teramo, Italy
Accepted 2014 May 6. Received 2014 May 6; in original form 2014 April 5
ABSTRACTWe present the results of a photometric search for variable stars in the core of the Galacticglobular cluster Messier 4 (M 4). The input data are a large and unprecedented set of deepHubble Space Telescope WFC3 images (large programme GO-12911; 120 orbits allocated),primarily aimed at probing binaries with massive companions by detecting their astrometricwobbles. Though these data were not optimized to carry out a time-resolved photometricsurvey, their exquisite precision, spatial resolution and dynamic range enabled us to firmlydetect 38 variable stars, of which 20 were previously unpublished. They include 19 cluster-member eclipsing binaries (confirming the large binary fraction of M 4), RR Lyrae and objectswith known X-ray counterparts. We improved and revised the parameters of some amongpublished variables.
Key words: techniques: photometric – binaries: general – stars: variables: general – globularclusters: individual: NGC 6121.
1 IN T RO D U C T I O N
Messier 4 (M 4), also known as NGC 6121 is the closest Galac-tic globular cluster (GC) at 1.86 kpc, having the second smallestapparent distance modulus after NGC 6397: (m − M)V = 12.68(Bedin et al. 2009). It is known to show no evidence for any central
� Based on observations collected with the NASA/ESA Hubble Space Tele-scope, obtained at the Space Telescope Science Institute, which is operatedby AURA, Inc., under NASA contract NAS 5-26555, under large programGO-12911.†E-mail: [email protected]
brightness cusp, despite being significantly older than its dynam-ical relaxation time (Trager, King & Djorgovski 1995). Further,the photometric binary fraction in the core of M 4 is among thehighest measured for a GC, reaching 15 per cent in the core region(Milone et al. 2012, compare with 2 per cent for NGC 6397). Thefine details of the role played by dynamical interactions betweenbinary stars in the delay of cluster ‘core collapse’ are still debated,with different competing theories proposed to explain them (seeHeggie & Hut 2003 for a review). As M 4 appears to be a perfectcase to test those theories, we proposed a Hubble Space Telescope(HST) large programme entitled ‘A search for binaries with massivecompanions in the core of the closest GC M 4’ (GO-12911, PI:Bedin), which has been awarded 120 orbits and has already been
successfully completed. The main aim of our project is to probethat fraction of binary population which is undetectable by meansof usual photometric techniques, viz. the fraction that is made upof binaries composed of a main-sequence (MS) star and a massive,faint evolved companion (e.g. black hole, white dwarf, neutronstar). The employed technique is an astrometric search for wob-bles due to the motion of the bright component around the systembarycentre. In support of this programme, a set of 720 WFC3/UVIS(Wide Field Camera 3, Ultraviolet and VISual channel) imageshave been gathered over a baseline of about one year. The UVIS162 arcsec × 162 arcsec field of view (FOV) covers the whole coreof M 4 (whose radius is rc � 70 arcsec; Harris 1996) at every rollangle. Of course, such a massive data set can be exploited for alarge number of tasks other than the primary one. We will refer thereader to Paper I (Bedin et al. 2013) for a detailed description ofthe programme and for a discussion about other possible collateralscience.
M 4 is a cluster that has some desirable properties for photometricsearches of variables among Population II stars, viz. both its prox-imity and relatively low-density core. For this reason, it has beenintensively targeted since the beginning of the photographic andphotoelectric era (Leavitt & Pickering 1904; Sawyer 1931; Green-stein 1939; de Sitter 1947) up to more recent works which em-ployed CCD photometry, either ground based (Kaluzny, Thompson& Krzeminski 1997; Kaluzny et al. 2013a) or space based (Ferdmanet al. 2004). Besides a large number of known RR Lyrae (53, ac-cording to the online data base1 compiled by C. Clement), eclipsingbinaries and other ordinary variables, M 4 also hosts other less-common objects of interest, including an exotic planetary systemmade of a pulsar, a white dwarf (WD) and a 2.5 Mjup planet (Sigurds-son et al. 2003) and many X-ray sources (Bassa et al. 2004) whoseoptical counterparts show both periodic or irregular photometricvariability (Kaluzny et al. 2012).
In this study, we exploit the GO-12911 data set to extract 9410light curves of every well-measured, point-like source in the M 4core, spanning from the horizontal branch down to the lower MS. Weaim at discovering new variable stars and at refining the parametersof some others that were previously published; this includes the firmidentification of a few objects for which the physical nature and/orthe cluster membership was classified as ‘uncertain’ in the past. Wedescribe in Section 2, the criteria adopted to select the input list,the procedures to correct the light curves by means of differentiallocal photometry, and the specific algorithms employed to performthe search for periodic and irregular variability and to sift the mostsignificant candidates. Then, in Section 3, we present our list of 38high-confidence variables, along with a discussion of some notableindividual cases. The overall statistics of our set, and in particularabout its completeness limits and biases, is eventually discussed inSection 4.
2 DATA A NA LY SIS
The full GO-12911 data set was gathered during 120 HST orbits,arranged in 12 epochs made of 10 HST visits each, where each visitis one orbit. Each orbit is filled with five 392–396 s exposures inthe blue filter F467M (except for 11 isolated frames for which theF467M exposure time was set to 366 s), and one additional 20 sexposure through a red F775W filter at the beginning of the orbit.
1 http://www.astro.utoronto.ca/∼cclement/cat/listngc.html (Clement et al.2001, last update 2009).
The choice of such unorthodox filters was driven by the astrometricrequirements of our project. The intermediate band F467M yields amore monochromatic-like point spread function (PSF), less prone tocolour-dependent systematic errors. For the same reason, the Sloani′-like F775W filter was preferred over the more commonly usedF814W thanks to its better characterized astrometric solution. Its∼1000 Å cut on the red tail does not imply a significant flux loss,because there the total transmission is very low. The F467M filteralso has the advantage of suppressing the contaminating light ofPSF haloes from red giants.
The first visit occurred on 2012 Oct 9, followed by a 100 d gapand then by 11 other visits regularly spaced at an ∼24 d cadence.In this work, we will focus on a homogeneous subset of 589 ‘deep’(392–396 s) F467M images, in order to take advantage of a densersampling and smaller flux contamination from giants. Data reduc-tion was carried out by modelling an effective PSF (ePSF; Anderson& King 2000) tailored on each frame. Details about the ePSF ap-proaches can be found in Paper I and references therein. Propermotions were derived by matching our data with Advanced Camerafor Surveys (ACS) astrometry by Sarajedini et al. (2007, GO-10775,PI: Sarajedini), over a baseline of about six years.
It is worth noting that the codes employed are able to extractacceptable photometry even on stars brighter than saturation by col-lecting the charge bled along the columns of the detector (Gilliland2004; Anderson et al. 2008). This is possible thanks to the excel-lent capability of WFC3/UVIS to conserve the flux even after thepixel full-well is exceeded (Gilliland, Rajan & Deustua 2010). Eachunsaturated star in each exposure was measured by adding up theflux within its central 5 × 5 pixels, then dividing by the fractionof the star’s light that should have fallen within the aperture (basedon the PSF model and the PSF-fitted position of the stars withinits central pixel). The aperture for saturated stars started with this5 × 5 aperture, but we also had to include all contiguous pixels thatwere either saturated or neighbouring saturated pixels. The totalflux was then the flux of the star through the aperture divided bythe fraction of the PSF determined to lie within the aperture. In thisway, we were able to determine the photometry of the saturated andunsaturated stars in the same system. Fig. 1 shows that the absoluteprecision of the saturated stars is not as good as that for the unsat-urated stars, since the local zero-point (LZP) and global zero-point(GZP) are constructed to correspond to the 5 × 5 pixel aperture, notthe variable aperture for saturated stars. Nevertheless, the smooth-ness of our colour–magnitude diagram (CMD; Fig. 3) across theF467M saturation boundary at −13.75 indicates that there are nosystematic differences between photometry for the saturated andunsaturated stars. The reliability of this approach is shown by thequality of the light curves for the 13 RR Lyrae stars (see Section 3.1for details).
Our initial input list was constructed by requiring the detectionfor each given source in at least 100 out of 589 frames, in or-der to get light curves spanning a phase coverage large enough toextract a meaningful period analysis from them. This constraintleft us with 9410 sources, all brighter than instrumental magnitudeF467M � −4, corresponding to about 40 detected photoelectrons.On the bright side, the most luminous stars reach F467M � −17.5(corresponding to V � 12.5: Fig. 1, upper-left panel). This meansthat the dynamic range of our data set spans more than 13 mag, en-abling us to measure stars which are usually saturated and neglectedin most surveys.
Most sources among our detections are single, point-like sourcesbelonging to M 4. A small fraction of the sample, however, ismade of galaxies, extended objects, unresolved stellar blends and
Figure 1. Left, upper panel: photometric error σp as a function of instrumental magnitude F467M, measured on all stars with three different correctionalgorithms: none (‘RAW’, red points), global zero-point (‘GZP’, green) and local zero-point (‘LZP’, blue). Saturation occurs at F467M � −13.75. Left, lowerpanel: ‘improvement’ as a function of F467M, i.e. the per cent reduction of rms compared to raw light curves, averaged on 0.25 mag bins. Colours are coded asabove. Right: median value of the fit quality parameter qfit as a function of F467M, all light curves (black circles). Variable stars found by our study (Table 1)are marked with red stars.
instrumental artefacts. These can be identified by looking at theqfit parameter, a diagnostic value that is related to the goodness ofthe ePSF fit (Anderson et al. 2008). As the mean 〈qfit〉 of a lightcurve is a monotonically increasing function of magnitude (Fig. 1,right-hand panel), a reliable way to identify badly measured outliersis to compare it with its median value evaluated over magnitude bins.We anticipate that, after the vetting procedure, all the variable starsdiscussed here are high-confidence point-like sources.
The observing strategy behind the GO-12911 programme was op-timized for performing high-precision astrometry. In order to modeland correct all the distortion terms of the astrometric solution, theimages were gathered by setting a large-dither pattern of 50 pointsand changing the telescope roll angle within each astrometric epoch.Stars fall on completely different physical pixels on most frames.While this is a winning choice for the main goal of programme,it poses some issues when trying to extract accurate time-resolvedphotometry. Even when the PSFs are carefully modelled, this ap-proach amplifies the effect of flat-field residual errors, intrapixeland pixel-to-pixel inhomogeneities, and other position-dependenteffects. As a consequence, subtle second-order systematics are in-troduced in our photometry, as is evident by examining the rawlight curves which share common trends whose shape and ampli-tude depend on the sky region analysed. A similar behaviour wasalso observed on data from the ACS/WFC in our previous workon NGC 6397 (Nascimbeni et al. 2012). Our approach to minimizesuch systematics is based on correcting differential light curves bysubtracting a LZP, evaluated individually for each target star andeach frame.
2.1 Global differential photometry
Before performing an LZP correction, an intermediate and straight-forward step is applying a GZP correction. In what follows, weindex the individual frames with variable i, the 9410 target starswith the variable k and the subset of sources chosen as comparison
stars with j. Individual data points from target/reference light curveswill be then identified by mi, k and mi, j, respectively. The notation〈x〉y represents the averaging of x over the index y. Unless other-wise noted, averaging is done by evaluating the median and settingas the associated scatter σ 〈x〉 the 68.27th percentile of the absoluteresiduals.
As a first step, we chose a common set of reference sources. Theseare required to be bright, non-saturated (−13.75 < F467M < −10),point-like and well-fitted (qfit within 2σ from the median qfit
of all the stars having similar magnitude; this ensures that extendedsources and blends are discarded). We also required that they aredetected and measured on a minimum number of frames Nmin = 500over 589, as a reasonable compromise between completeness andFOV coverage. This left us with 1485 reference stars. For each ofthem, we computed the median raw magnitude 〈mi, j〉i by iterativelyclipping outliers at 2σ ; then each reference raw light curve mi, j wasnormalized by subtracting 〈mi, j〉i from it. A global ‘trend’ τ i wascalculated for each frame i by taking the 2σ clipped median of allavailable mi, j − 〈mi, j〉i. The quantity τ i is the GZP correction to beapplied to each point mi, k belonging to target light curves
The pre-normalization procedure enables us to estimate τ i with-out biases, even if a small subset of reference stars is lacking froma given frame. On the other hand, median statistics, as opposedto arithmetic means and rms, proved to be robust enough againstoutliers.
If one plots the photometric scatter σ 〈m〉 and σ〈m′〉 as a functionof magnitude (Fig. 1, upper-left panel, red versus green points), it isclear that σ〈m′〉 < σ〈m〉 especially on bright stars (−13.5 < F467M <
−10). The average decrease in rms is up to 15 per cent at F467M �−13 (Fig. 1, lower-left panel). GZP correction is therefore effectivewhen compared to raw photometry. Still, upon visual inspection,spatial- and magnitude-dependent systematics are still present on
the bright side of our sample and require a more sophisticatedcorrection.
2.2 Local differential photometry
In order to build a set of suitable reference light curves to evaluate anLZP correction, one needs to trim down the list of comparison starsby rejecting variables and badly behaved sources. First, we consid-ered the distribution of GZP-corrected scatter σ〈m′〉 as a function of〈m′
i,j 〉i , evaluating its median and scatter over magnitude bins; theneach star more than 4σ off the median σ〈m′〉 was discarded from thereference set. The ‘loose’ 4σ threshold is justified by the need of notrejecting stars which could share common systematics with respectto other target stars; in that case their inclusion in the reference setwould be the only way to correct such systematics.
For each pair of target star k and reference star j, we constructeda differential light curve by subtracting their raw magnitudes mi, k
and mi, j on each frame i where both stars are detected. Then weconsidered the distribution of the absolute residuals around 〈mi, k −mi, j〉i, and define the scatter σ jk as the 68.27th percentile of suchresiduals. The quantity σ jk is an empirical estimate of how muchthe reference star j is a ‘good’ reference for the target k. We can thenassume the quantities wjk = 1/σ 2
jk as initial weights to compute amore accurate ZP correction for a given target k.
Since we want the correction to be local, we also multiply theweights by a factor Djk which is dependent on the relative on-sky position �2
jk = (xj − xk)2 + (yj − yk)2 between the referencestar (xj, yj) and the target star (xk, yk). To avoid using a referencestar too close to the target, which could therefore be blended orcontaminated, Djk is forced to zero within r0. Outside r0, we choseto parametrize Djk as a unitary factor up to an inner radius rin, andthen as a smooth function which decreases exponentially from oneto zero with a rout − rin scale radius (i.e. the factor Djk is 1/e at rout)
Djk =
⎧⎪⎪⎪⎨⎪⎪⎪⎩
0 if �jk < r0
1 if r0 ≤ �jk ≤ rin
exp
[−
(�jk−rin
rout−rin
)2]
if �jk > rin.
(2)
A similar weight factor Mjk is imposed on the magnitude differ-ence φjk = |mj − mk|, as we expect that systematics due to non-linearity and background estimation are magnitude dependent. Theflux boundaries are fin and fout, respectively:
Mjk =
⎧⎪⎨⎪⎩
1 if φjk ≤ fin
exp
[−
(φjk−fin
fout−fin
)2]
if φjk > fin.(3)
Summarizing, the final weights are given by multiplying theabove factors:
Wjk = (1/σ 2
jk
)DjkMjk . (4)
The LZP correction τ ′i is evaluated as for the GZP correction (equa-
tion 1), but this time using the weighted mean of magnitudes of ourset of reference stars instead of an unweighted median, where theweights are assigned as Wjk. A 3σ clip is applied on each image ito improve robustness.
Our approach gives larger weights to reference stars which (1)produce a smaller scatter on the target light curve; (2) are geometri-cally closer to the target as projected on the sky; (3) have a magni-tude similar to that of the target. Of course, this approach could beeasily generalized by introducing weights based on other externalparameters, such as colour or background level, for instance.
The five input parameters r0, rin, rout, fin, fout have to be chosenempirically. After some iterations, we set r0 = 20 pix, rin = 200 pix,rout = 300 pix, fin = 1.0 mag, fout = 1.75 mag. The improvementof the LZP correction over the GZP one is shown in the left-handpanel of Fig. 1. In the bright, non-saturated end of our sample(F467M � −13) the rms is lowered by 10–25 per cent on averagewhen compared to GZP-corrected and raw photometry, respectively.On the faintest targets, GZP performs slightly better than LZP be-cause photon noise dominates and GZP is not forced to discardvery bright stars as LZP does. For each target, we chose to apply anoptimal correction which outputs the light curve having the lowestscatter among the raw one and the GZP- or LZP-corrected ones.From here on, all procedures are carried out on such optimal lightcurves.
2.3 Variable-searching procedures
A battery of software tools to detect both periodic and non-periodic photometric variability was applied to all 9410 correctedlight curves. These tools included period-searching algorithmssuch as the classical Lomb & Scargle periodogram (LS; Lomb1976; Scargle 1982) and its generalized version GLS (Zechmeis-ter & Kurster 2009); the Analysis of Variance periodogram (AoV;Schwarzenberg-Czerny 1989); the Box-fitting Least-Squares peri-odogram (BLS; Kovacs, Zucker & Mazeh 2002). The latter is themost sensitive to eclipse-like event, such as those expected from de-tached eclipsing binaries and planetary transits. A second class ofdiagnostics was exploited to search for more general types of vari-ability: the alarm variability statistic as described by Tamuz, Mazeh& Zucker (2005), the overall scatter (based on robust median statis-tics as defined at the beginning of Section 2.1) as a function ofmagnitude, and the rms after each of the 12 astrometric epochs hasbeen averaged on a single bin, to catch the effects of long-termvariability.
We already mentioned that our data set is not optimized to searchfor periodic variability. One of the most limiting factors is the non-regular cadence, as each astrometric epoch is separated by 24 d.These temporal gaps introduce many spurious frequencies in theperiodograms, making the recovery of the true (astrophysical) pe-riod problematic, especially for signals at P < 24 d where mostof the variables are expected to be. We illustrate this by injectingnoise-free sinusoids over the 589-images time baseline of our WFC3data set, and then recovering the signal through a GLS periodogramon the synthetic light curve (Fig. 2). In both cases at Pinj = 0.3and 4.0 d, we get a ‘comb’ of periodogram peaks instead of a sharpspike, as it would be expected in an optimal sampling regime. Whenrandom noise and systematic errors are accounted for, period recov-ering gets harder, and the 24 d alias induced by sampling becomesthe most significant period. For this reason, we split our searchover two period ranges: 0.1–20 and 20–200 d, analysing each setindependently.
To visually supervise all the individual outputs of the analysisdescribed above on more than 9000 targets would be too muchtime-consuming and prone to biases. Instead, we selected a shortlist of candidate variables by running the very same analysis on aset of synthetic light curves, sampled at the same epochs as the realdata but after having randomly shuffled the magnitude values. Inthis way, noise and sampling cadence are preserved, while phasecoherence is broken: the resulting ‘synthetic’ analysis represents theexpected output when an intrinsic signal is not present. We focusedon the distribution of diagnostics such as
Figure 2. Noise-free window function computed over the temporal baselineof our data set; the injected periods are Pinj = 0.3 d (upper panel) andPinj = 4.0 d (lower panel).
(i) the periodogram power for the LS, GLS and AoV algorithm(as defined in the original papers, i.e. PX by Scargle 1982, p(ω)by Zechmeister & Kurster 2009, and � by Schwarzenberg-Czerny1989, respectively);
(ii) the SN and SDE statistics (Kovacs et al. 2002) and the signal-to-pink noise ratio (as defined by Pont, Zucker & Queloz 2006 andimplemented by Hartman et al. 2008) for the BLS periodogram;
(iii) the alarm index A (Tamuz et al. 2005) and the visit-binnedand unbinned rms as a function of magnitude, defined as above.
For each of the above diagnostics, the output distribution from thereal data was compared with the results from the synthetic lightcurves, selecting all targets which fall at least 3σ outside the latterdistribution. This gave us a list of 401 candidates which were indi-vidually inspected. Most of them turned out to be spurious, due to thetarget being blended, contaminated, or part of an extended source.Very often false positives came from sources with bad photometryon a single visit due to the star falling on a bad pixel or too closeto the detector edges. The latter case was the most frequent causeof false positives detected at periods around the 12 or 24 d alias.
3 R ESULTS
After the vetting process, only 38 variables survived. They are listedin Table 1; their light curves are plotted in Figs 4 and 5, and the cor-responding data points are tabulated in Table 2. All of them appearto be isolated, point-like sources, following a visual inspection ofthe images. This is also confirmed by their qfit diagnostic, whichis perfectly consistent with the median qfit of well-measured starsof similar magnitude (Fig. 1, right-hand plot; variables are markedwith red stars). Their detected periods are clearly distinct from thetypical periods due to aliasing or instrumental effects, such as the96 min orbital period of HST or the 24 d separation between con-secutive visits. For the reasons above, we can identify all those 38stars as genuine astrophysical variables. In Table 1, we also re-port the Johnson V-band magnitude of each variable (obtained by
cross-matching our catalogue with that by Sarajedini et al. 2007)and we identify which stars are matched within a 2σ error ellipsewith an X-ray source from the Bassa et al. (2004) catalogue. Westress out that the reported V magnitudes represent the average ofthe values obtained by Sarajedini et al., not an intensity-weightedaverage throughout the phase of our light curves.
The membership of our variables with respect to M 4 can beassessed with a very high level of confidence by inspecting theproper motion vector–point diagram (VPD), where stars belongingto the cluster and those in the general field appear extremely wellseparated (Fig. 3, upper-left plot). To our purposes, the VPD does notneed to be calibrated in physical units (arcsec yr−1 proper motion);instead, we simply plot the displacement in pixels measured over thebaseline between the WFC3 observations and the first astrometricACS epoch (∼6 yr). We found that nearly all variables are clustermembers with the only exceptions being ID# 3407 and 3708. Asexpected, most variables found at magnitudes fainter than the clusterturnoff turned out to be eclipsing binaries, both of contact (cEB)and detached (dEB) subtypes. On most cases, this classification isalso supported by their position on the CMD, which is shifted upto ∼0.75 mag upwards with respect to single, unblended MS stars(Fig. 3). A discussion of individual cases follows.
3.1 Notes on individual objects
Known RR Lyrae: ID# 1076, 1134, 1497, 2594, 4363, 6285, 6394,6458, 6954, 8077, 8798. These are RR Lyr variables known sincea long time (Greenstein 1939, re-identified by Shokin & Samus1996), but whose periods are here determined with much more pre-cision given the 1 yr temporal baseline. The discrimination betweenRRab (ID# 1076, 1134, 4363, 6394, 6458, 6954, 8077, 8798) andRRc (1497, 2594, 6285) subtypes is obvious. Our classification isconfirmed by their position in the CMD (Fig. 3, right-hand panels),with RRab and RRc member being clearly separated by the RRLyrae gap. The amplitudes of ID# 6285 and 8077 change signifi-cantly through the series, due possibly to the Blazhko effect (Kovacs2009).
New RR Lyrae: ID# 6858, 6955. These are two very close(1.6 arcsec) RR Lyr variables having similar magnitude (V = 13.24versus 13.39). Such an unusual pair is mostly blended on ground-based images, so it is not surprising that it was classified by Green-stein (1939) as a single RR Lyr with a problematic light curve (C40)and a poorly constrained period. Other studies recognized it as avisual binary but failed at discovering the true nature of both sources(de Sitter 1947); therefore, C40 has been neglected in many follow-up works on RR Lyrae. We identified both stars as RRc subtypeswith periods P � 0.39 and 0.29 d, respectively.
Blue stragglers: ID# 1600 and 7820 are without any doubt clustermembers based on their proper motions, and are located in the ‘bluestraggler’ region of the CMD. ID# 1600 was already known asa short-period, near equal-mass contact eclipsing binary (Kaluznyet al. 1997). ID# 7820 also is a contact binary, reported here forthe first time. Its periodic modulation at P � 0.66 d is detected athigh significance. Its primary and secondary minima, showing veryunequal depths, suggest a much lower mass ratio than ID# 1600.
Known contact EBs: ID# 3401, 3407, 5430, 6807 are alreadylisted in the Clement et al. (2001) catalogue. They are located closeto the turnoff region, with very well-defined primary and secondaryminima and periods spanning 0.26–0.30 d. Among these, ID# 3407is the only field star, clearly separated from the cluster in the propermotion (PM) diagram; also it is an X-ray source catalogued as CX13by Bassa et al. (2004).
Notes. The columns give: a progressive number N, the ID code of the source according to our catalogue, the equatorial coordinates α
and δ at epoch 2000.0, the instrumental magnitude in F467M and the standard Johnson V magnitude from Sarajedini et al. (2007), amembership flag derived from the VPD, the variability class assigned by our study, the most probable photometric period P (wheredetectable), the cross-references to the variable catalogues by Kaluzny et al. (2013a, letter K) and Clement et al. (2001, letter C),and some notes. Notes are codified as follows: MS = main-sequence star, BSEQ = binary sequence star (between fiducial MS andMS+0.75 mag), HB = horizontal branch, BSS = blue straggler star, CX = X-ray source from the catalogue by Bassa et al. (2004),TO = turn-off star, NM = not a cluster member. A few periods of dEBs, marked with a ‡, have been doubled with respect to thebest-fitting periodogram solution, following astrophysical arguments (see Section 3.1 for details); two cases are ambiguous, and markedwith an additional question mark. The two variables marked by † in the X-ref field were once classified as a single, atypical RR Lyr(Clement et al. 2001 and references therein).
Detached EBs: ID# 760, 2108, 3708, 5286, 5460, 6873, 7202are detached eclipsing binaries, all identified as cluster members byPMs with the only exception of ID# 3708. Among them only ID#5460 was previously published (as K66 by Kaluzny et al. 2013a).All of them lie in the upper part of the binary MS, i.e. are systemswith high mass ratios (q ≈ 1). For that reason, their phased lightcurves are expected to show two eclipses of similar depth betweenphases 0 and 1. But the period-search algorithms does not know thisand therefore might find periods of half the true duration with light
curves showing only one eclipse between phases 0 and 1. In somecases, such as for ID# 2108, we have no way of knowing the trueperiod with the current data because of holes in the phased lightcurves where an eclipse might be happening. In other cases, suchas for ID# 5286, the phase coverage seems sufficient to rule out thepresence of a second eclipse at the period found, which suggeststhat the true period is twice as long. Based on such considerations,we give the most likely true periods in Table 1. ID# 2108 also is anX-ray source (CX 28; Bassa et al. 2004), but its light curve shows no
Notes. This table is published in its entirety as a machine-readable table in the onlineversion of this article and the Centre de Donees Strasbourg (CDS) at http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/MNRAS/. A portion is shown here for guidance regarding itsform and content. The columns give: the ID code of the source according to our catalogue(see Table 1), the mid-exposure time in the BJD–TDB time standard (Eastman, Siverd &Gaudi 2010), the instrumental magnitude in F467M and the associated photometric error,the x and y centroid position on the chip, and the qfit quality parameter.
sign of stellar activity or interaction. We set the period of ID# 3708as a lower limit (P > 6.47 d) since only one eclipse is detectable inour series.
New contact and generic EBs: ID# 2316, 3153, 3487, 3575. Thelight curves of ID# 2316 and 3153 show an anomalous amount ofscatter despite being isolated and well-measured (low qfit); thiscould be ascribed to starspot-induced variability by one or bothcomponents of the eclipsing binary. ID# 3487 is a much fainter EBin the lower MS, observed at low S/N but with recognizable minimaand maxima.
Probable EBs: ID# 1001, 2992, 3236, 3627. ID# 1001 shows asharp ∼0.1 mag eclipse overimposed on a pseudo-sinusoidal mod-ulation. If the modulation is interpreted as caused by a ‘hotspot’ orpersistent active region then the eclipse appears to be out of phase byabout 0.25 (assuming circular orbits, and spin–orbit alignment). Nosecondary minimum is detected. Light curves of ID# 2992, 3236,3627 share similar amplitudes (0.05–0.1 mag) and an excess of pho-tometric scatter, but their position in the CMD makes a cEB/dEBclassification plausible. ID# 3236 (=CX3) and 3627 (=CX20) arealso matched to X-ray sources.
Unclassified /uncertain: ID# 275, 7864, 8081, 9050. The lightcurve of ID# 275 is clearly periodic with a ‘double-wave’ shapeand minima of similar depths. Anyway, its period P � 0.18 d issmaller than the usual ∼0.22 d cut-off found for MS+MS eclipsingbinaries (Norton et al. 2011) and its position on the CMD is veryclose to the MS ridge, disproving the presence of companions withhigh q. On the other hand, ID# 275 could be a new member of therecently discovered class of ultra-short-period M dwarf binaries,first introduced by Nefs et al. (2012). ID# 7864 is a known variableand X-ray source (K52; CX8), and is much brighter than the upperbinary sequence envelope, revealing itself as an interacting and/orhigher multiplicity system. This is confirmed by its light curve,showing a strong P � 0.77 d periodicity but also a heavily disturbedsignal, as already noticed by Kaluzny et al. (2013a). A similar lightcurve is detected at P � 0.97 d on the previously uncataloguedID# 8081, also an X-ray source (CX11). ID# 9050 is even morepeculiar: just as ID # 275, the signal is a clean ‘double-wave’ atP � 0.18 d, again an unusually short period for a cEB, but fur-thermore its position on the CMD is slightly bluer than the MS,suggesting a possible binarity with a bright WD. Only a targetedfollow-up could reveal more about the nature of this target.
4 D I S C U S S I O N A N D C O N C L U S I O N S
In the previous sections, we described how we performed a searchfor photometric variability among a sample of 9410 stars in a fieldimaged by HST on the core of the GC M 4. Such a search yielded 38variable stars; all but two are cluster members, and 20 are reportedhere for the first time. Quite surprisingly, two newly (re-)classifiedsources are a pair of bright but blended RR Lyrae, whose true naturehas been unveiled by the superior angular resolution of space-basedimaging. A few candidates cannot be assigned to standard variabilityclasses, being aperiodic, multiperiodic, or lying in unusual regionsof the CMD.
We did not detect any signal which could be interpreted as a tran-sit by planet-sized objects orbiting around solar-type stars (i.e. box-shaped eclipses having photometric depth smaller than 0.03 mag).Many intrinsic factors in our data set are strongly limiting a transitsearch, above all sparse temporal sampling (which decreases phasecoverage, and worsens the effects of long-term stellar variability)and large-scale dithering (which boosts position-dependent system-atic errors). As only planets among the relatively rare ‘hot Jupiter’class are within reach of such a search, the statistical significance ofour null detection is probably very low. We will investigate this fur-ther in a forthcoming paper of the ‘M 4 core project’ series focusedon transit search, which will also analyse time series photometryfrom the parallel ACS fields.
The overall completeness level of our search is difficult to quan-tify without posing very special assumptions about the shape andperiod of the photometric signal to be recovered. However, we notethat we firmly detected variables having photometric amplitudes ofthe order of a few hundredths of magnitude even in the fainter halfof our sample (such as ID# 1001, 3487, 3575, 5286). Even thoughperiodograms are aliased at some characteristic frequencies by theparticular sampling cadence of our data (Fig. 2), phase coverage iscomplete up to periods of about six days. Merging the picture, thismeans that eclipsing contact binaries should be detectable with acompleteness factor close to 1, with only rare exceptions expectedfrom very grazing systems, or from binaries with mass ratios q muchsmaller than 1.
About half of the reported variables (21, of which 19 arehigh-confidence cluster members) are certain or probable eclips-ing binaries. As we detected 19 EBs among 5488 MS stars with
Figure 3. Proper motion vector–point and colour–magnitude diagrams (VPD, CMDs) of M 4, where the detected variables have been highlighted. Upper left:x and y proper motion displacements in physical pixels, for each analysed star (grey dots) and detected variables (blue crosses). Among the latter, only ID#3407and 3708 appear to not be cluster members. Lower right: instrumental F467M, F775W CMD of M 4 from our data set. Variables are marked with blue crosses.Regions within green boxes (A, B, C, D) are zoomed and displayed in the corresponding remaining panels, and labelled according to the legend.
−12.75 < F467M < −7.0, or – restricting the magnitude range tobrighter targets – 16 EBs among 4080 MS stars with −12.75 <
F467M < −9.0, we estimate an observed EBs fraction of about0.3–0.4 per cent. This value is approximately consistent with themeasured photometric binary fraction in the core of 14.8 ± 1.4per cent (Milone et al. 2012), when allowance is made for the lowfraction of binaries which are expected to exhibit eclipses. Usingpopulation synthesis, Soderhjelm & Dischler (2005) show that thefraction of all F and G stars exhibiting eclipses with a depth of afew tenths of a magnitude and a period of a day is about 3 per cent.The population they studied had a binary fraction of 80 per cent,however, and so the corresponding result for the core of M 4 wouldbe expected to be about 0.5 per cent, i.e. close to our results. A moreprecise discussion depends on several factors, such as the details ofthe period distribution of the observed binaries, dynamical erosionof the binary population, and the initial binary distributions assumed
in the population synthesis. Indeed, the observations reported in thispaper are likely to be a useful constraint on our future dynamicalmodelling of M 4.
As a final remark, we note that the dEBs that are cluster memberscan potentially be used for obtaining precise cluster parameters,insights into multiple populations of the cluster and stellar evolu-tion tests in general (Paper I; Brogaard et al. 2012; Milone et al.2014). This requires however that the dEBs are bright enough forspectroscopic measurements. Based on our experience from dEBsin the open cluster NGC 6791, four of the dEBs we identify inM 4 (ID# 5460, 7202, 6873, and 2108) are within reach of currentspectroscopic facilities such as Ultraviolet and Visual Echelle Spec-trograph at the Very Large Telescope. Adding also the additionaldEBs found and analysed by Kaluzny et al. (2013b) makes a sampleof six dEBs in the turn-off and upper MS of M 4 with great poten-tial for improved cluster insights. The two low-mass dEB systems
Figure 4. Light curves of variables detected on our data set, folded on the most significant period found by periodograms (ID# 275-3627). Data points arerepeated twice over phase for clarity. Targets are sorted by ID# code. See Table 1 for coordinates and cross-referencing.
found on the lower MS (V � 22; ID# 760 and 5286) are too faintfor current spectroscopic facilities, but interesting potential targetsfor a future extremely large telescope. We note that M 4 will be inone of the fields of the K2 mission (Howell et al. 2014), and thatobserving these six dEBs with K2 would solve period ambiguitiesand provide full-coverage light curves valuable for their analysis.
AC K N OW L E D G E M E N T S
LRB, GP, VN, SO, AP and LM acknowledge PRIN-INAF 2012funding under the project entitled: ‘The M 4 Core Project with Hub-ble Space Telescope’. JA, AB, LU and RMR acknowledge supportfrom STScI grants GO-12911. KB acknowledges support from the
Figure 5. Light curves of variables detected on our data set, folded on the most significant period found by periodograms (ID# 3708-9050). Data points arerepeated twice over phase for clarity. Targets are sorted by ID# code. See Table 1 for coordinates and cross-referencing.
Villum Foundation. APM acknowledges the financial support fromthe Australian Research Council through Discovery Project grantDP120100475. MG acknowledges partial support by the NationalScience Centre through the grant DEC-2012/07/B/ST9/04412. VNacknowledges partial support from INAF-OAPd through the grant‘Analysis of HARPS-N data in the framework of GAPS project’(#19/2013) and ‘Studio preparatorio per le osservazioni della mis-
sione ESA/CHEOPS’ (#42/2013). LM acknowledges support fromthe European Union Seventh Framework Programme (FP7/2007-2013) under Grant Agreement #313014 (ETAEARTH). AC ac-knowledges support by the CARIPARO foundation through thegrant ‘Ricerca di pianeti extra-solari: nuove tecniche per trovarepianeti simili alla Terra’. Some tasks of our data analysis havebeen carried out with the VARTOOLS (Hartman et al. 2008) and
ASTROMETRY.NET codes (Lang et al. 2010). This research made useof the International Variable Star Index (VSX) data base, operatedat AAVSO, Cambridge, MA, USA.
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S U P P O RT I N G IN F O R M AT I O N
Additional Supporting Information may be found in the online ver-sion of this article:
Table 2. Light curves of the variables found (http://mnras.oxfordjournals.org/lookup/suppl/doi:10.1093/mnras/stu930/-/DC1).
Please note: Oxford University Press is not responsible for thecontent or functionality of any supporting materials supplied bythe authors. Any queries (other than missing material) should bedirected to the corresponding author for the paper.
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